XXXIII A AKD B] Introduction Ivii 



Illustration (i). A cable of 132'5 is suspended over the gap between two 

 towers of the same height, 115 feet apart. What will be the droop of the cable? 



;3 = 100^^^i?^^^=ll-52. 

 llo 



Table XXXIII A, gives us a = 21-62 = 100 subtense/chord. 



.'. subtense = 2162 x 115 



= 24-86. 

 Thus the droop is 24-86 ft. 



Illustration (ii). A catenary arch is to have a rise of 50 ft., centre line 

 measurement, and a span of 200. What is the length of the centre line ? 



a=100x 50/200 = 25-0, 

 but a = 25 by Table XXXII gives /3 = 15-1. " 



100 (arc — chord)/chord = 151. 

 .-. arc = 230-2 ft.* 



Illustration (iii). For some races the shape of the nasal bridge is very ap- 

 proximately a catenary. Thus if the nasal chord from dacryon to dacryon be 

 measured and also the tape measure from dacryon to dacryon, we obtain the 

 mesodacryal index /8. The tables enable us to pass to the mesodacryal index a, 

 and thus ascertain the na.sal subtense, which is slightly harder of direct measure- 

 ment than the arcual or tape measure. 



In the skull of a male gorilla the mesodacryal chord was 22-6 mm., and the 

 mesodacryal arc 30 mm. Determine the mesodacryal subtense 



^-100 30 -22-6 100 X 7-4 _ 



^ ^" 22-6 " 22-6 -•^^^*- 



Hence, from Table XXXII : 



a = 38-84 = 100 subtense/22-6. 

 .-. subtense = 22-6 x -3884 = 88 mm. 

 The actual value of the mesodacryal subtense measured on the skull was 

 8-7 mm. 



Abac XXXIV (p. 65) 



Diagram to find the Correlation Coefficient r from Mean Contingency on the 

 Hypothesis of a Normal Frequency Distribution. (Pearson : Drapers' Company 

 Research Memoirs, No. 1, " On the Theory of Contingency.") 



If rip, be the frequency in the cell of the pih column and 5th row of a correlation 

 or contingency table, and m.p be the total frequency in the pi\\ column, ?i, the 



* Should there be any use for this table for constructional purposes, which there ought to be when the 

 value of the catenary arch is more fully recognised, I will in a later edition of this work give the value 

 of u corresponding to each ^, so that the parameter c can be at once read off and the form of the arch 

 readily plotted. It might also be desirable to give the values of o and jS to two decimal places. We 

 have these data in our MS. copies. 



B. ft 



